Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
	static final int M = 1000000007;

	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long[] readArrayLong(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		int[] readArrayInt(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	// sorting template
	static void sortLong(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

	static void sortInt(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

	static class Graph {
		private ArrayList<Integer> adj[];
		public String s;
		public String dpch;

		Graph(int n) {
			adj = new ArrayList[n + 1];
			for (int i = 1; i <= n; i++) {
				adj[i] = new ArrayList<>();
			}
		}

		void addEdges(int u, int v) {
			adj[u].add(v);
			adj[v].add(u);
		}
	}

	static class Pair<F, S> {
		F first;
		S second;

		Pair(F first, S second) {
			this.first = first;
			this.second = second;
		}

		public F getFirst() {
			return this.first;
		}

		public S getSecond() {
			return this.second;
		}
		// Sort on basis of first term, reverse p1.first and p2.first to sort in desc
		// Collections.sort(a, (p1, p2) -> (p1.first - p2.first));

		// Sort on the basis of second term, reverse p1.second and p2.second to sort
		// in
		// desc
		// Collections.sort(a, (p1, p2) -> (p1.second - p2.second));
	}

	static long __gcd(long a, long b) {
		if (b == 0)
			return a;
		return __gcd(b, a % b);
	}

	public static int timer, bridges;
	public static int[] in, low;
	static ArrayList<Pair<Integer, Integer>> ans;

	private static HashMap<Integer, Integer> getHash(int[] a) {
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int i : a) {
			hm.put(i, hm.getOrDefault(i, 0) + 1);
		}
		return hm;
	}

	public static void main(String[] args) throws IOException {
		FastScanner fs = new FastScanner();
		//int t = fs.nextInt();
		 int t = 1;
		StringBuffer res = new StringBuffer();
		for (int tt = 1; tt <= t; tt++) {
			int n = fs.nextInt();
			int[] a = fs.readArrayInt(n);
			// Set<Long> s = new HashSet<>();
			// for (long i : a)
			// s.add(i);
			// if (s.size() == 1) {
			// res.append("YES\n");
			// } else {
			// long[] f = new long[n];
			// long[] b = new long[n];
			// f[0] = a[0];
			// b[n - 1] = a[n - 1];
			// for (int i = 1; i < n; i++) {
			// f[i] = a[i] ^ f[i - 1];
			// }
			// for (int i = n - 2; i >= 0; i--) {
			// b[i] = a[i] ^ b[i + 1];
			// }
			// boolean flag = false;
			// for (int i = 0; i < n - 1; i++) {
			// if (f[i] == b[i + 1]) {
			// flag = true;
			// break;
			// }
			// }
			// res.append(flag ? "YES\n" : "NO\n");
			// }
			int sum = 0;
			for (int i = 0; i < n; i++) {
				sum += a[i];
			}
			if (sum % 2 != 0) {
				res.append(0).append("\n");
			} else {

				sum = sum / 2;
				boolean subset[][] = new boolean[sum + 1][n + 1];
				for (int i = 0; i <= n; i++)
					subset[0][i] = true;
				for (int i = 1; i <= sum; i++)
					subset[i][0] = false;
				for (int i = 1; i <= sum; i++) {
					for (int j = 1; j <= n; j++) {
						subset[i][j] = subset[i][j - 1];
						if (i >= a[j - 1])
							subset[i][j] = subset[i][j] || subset[i - a[j - 1]][j - 1];
					}
				}
				if (subset[sum][n]) {
					int gcd = a[0];
					for (int i = 1; i < n; i++) {
						gcd = (int) __gcd(gcd, a[i]);
					}
					for (int i = 0; i < n; i++) {
						a[i] /= gcd;
					}
					int ans = -1;
					for (int i = 0; i < n; i++) {
						if (a[i] % 2 != 0) {
							ans = i + 1;
							break;
						}
					}
					res.append(1).append("\n").append(ans).append("\n");
				} else {
					res.append(0).append("\n");
				}
			}
		}
		System.out.println(res);
	}
}